Nonlinear force-free field modeling of a solar active region using SDO/HMI and SOLIS/VSM data

We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to model the force-free coronal field above a solar active region, assuming magnetic forces to dominate. We take measurement uncertainties caused by, e.g., noise and the particular inversion technique into account. After searching for the optimum modeling parameters for the particular data sets, we compare the resulting nonlinear force-free model fields. We show the degree of agreement of the coronal field reconstructions from the different data sources by comparing the relative free energy content, the vertical distribution of the magnetic pressure and the vertically integrated current density. Though the longitudinal and transverse magnetic flux measured by the VSM and HMI is clearly different, we find considerable similarities in the modeled fields. This indicates the robustness of the algorithm we use to calculate the nonlinear force-free fields against differences and deficiencies of the photospheric vector maps used as an input. We also depict how much the absolute values of the total force-free, virial and the free magnetic energy differ and how the orientation of the longitudinal and transverse components of the HMI- and VSM-based model volumes compares to each other.Comment: 9 pages, 5 figure

The Influence of Spatial Resolution on Nonlinear Force-Free Modeling

The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting.Comment: Accepted to ApJ; comments/corrections to this article are welcome via e-mail, even after publicatio

Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force

Context: In the linear, β = 0 MHD regime, the transient properties of magnetohydrodynamic (MHD) waves in the vicinity of 2D null points are well known. The waves are decoupled and accumulate at predictable parts of the magnetic topology: fast waves accumulate at the null point; whereas Alfvén waves cannot cross the separatricies. However, in nonlinear MHD mode conversion can occur at regions of inhomogeneous Alfvén speed, suggesting that the decoupled nature of waves may not extend to the nonlinear regime. Aims: We investigate the behaviour of low-amplitude Alfvén waves about a 2D magnetic null point in nonlinear, β = 0 MHD. Methods: We numerically simulate the introduction of low-amplitude Alfvén waves into the vicinity of a magnetic null point using the nonlinear LARE2D code. Results: Unlike in the linear regime, we find that the Alfvén wave sustains cospatial daughter disturbances, manifest in the transverse and longitudinal fluid velocity, owing to the action of nonlinear magnetic pressure gradients (viz. the ponderomotive force). These disturbances are dependent on the Alfvén wave and do not interact with the medium to excite magnetoacoustic waves, although the transverse daughter becomes focused at the null point. Additionally, an independently propagating fast magnetoacoustic wave is generated during the early stages, which transports some of the initial Alfvén wave energy towards the null point. Subsequently, despite undergoing dispersion and phase-mixing due to gradients in the Alfvén-speed profile (∇c_A ≠ 0) there is no further nonlinear generation of fast waves. Conclusions: We find that Alfvén waves at 2D cold null points behave largely as in the linear regime, however they sustain transverse and longitudinal disturbances - effects absent in the linear regime - due to nonlinear magnetic pressure gradients

“I’ve got somebody there, someone cares”: what support is most valued following a stroke?

Purpose: There is often a need for increased support following a stroke. This study explored what types of support are provided by different network members, and what support functions are most valued. Methods: Adults with first stroke were recruited from a stroke unit, and participated in in-depth interviews 8-15 months post stroke. Framework Analysis was used to build thematic and explanatory accounts of the data. Results: Twenty-nine participants took part. Main themes to emerge were: the spouse was the most important provider of support; children were a relatively stable source of support, although many participants expressed reservations about worrying a child; relatives and friends typically provided social companionship and emotional support rather than on-going practical support. The only universally valued support function was the sense that someone was concerned and cared. Other valued functions were: social companionship including everyday social ‘chit chat’; practical support provided sensitively; and, for many, sharing worries and sensitive encouragement. The manner and context in which support was provided was important: support was easiest to receive when it communicated concern, and was part of a reciprocal, caring relationship. Conclusions: As well as measuring supportive acts, researchers and clinicians should consider the manner and context of support

Chromospheric seismology above sunspot umbrae

The acoustic resonator is an important model for explaining the three-minute oscillations in the chromosphere above sunspot umbrae. The steep temperature gradients at the photosphere and transition region provide the cavity for the acoustic resonator, which allows waves to be both partially transmitted and partially reflected. In this paper, a new method of estimating the size and temperature profile of the chromospheric cavity above a sunspot umbra is developed. The magnetic field above umbrae is modelled numerically in 1.5D with slow magnetoacoustic wave trains travelling along magnetic fieldlines. Resonances are driven by applying the random noise of three different colours---white, pink and brown---as small velocity perturbations to the upper convection zone. Energy escapes the resonating cavity and generates wave trains moving into the corona. Line of sight (LOS) integration is also performed to determine the observable spectra through SDO/AIA. The numerical results show that the gradient of the coronal spectra is directly correlated with the chromosperic temperature configuration. As the chromospheric cavity size increases, the spectral gradient becomes shallower. When LOS integrations is performed, the resulting spectra demonstrate a broadband of excited frequencies that is correlated with the chromospheric cavity size. The broadband of excited frequencies becomes narrower as the chromospheric cavity size increases. These two results provide a potentially useful diagnostic for the chromospheric temperature profile by considering coronal velocity oscillations

Large amplitude oscillatory motion along a solar filament

Large amplitude oscillations of solar filaments is a phenomenon known for more than half a century. Recently, a new mode of oscillations, characterized by periodical plasma motions along the filament axis, was discovered. We analyze such an event, recorded on 23 January 2002 in Big Bear Solar Observatory H$\alpha$ filtergrams, in order to infer the triggering mechanism and the nature of the restoring force. Motion along the filament axis of a distinct buldge-like feature was traced, to quantify the kinematics of the oscillatory motion. The data were fitted by a damped sine function, to estimate the basic parameters of the oscillations. In order to identify the triggering mechanism, morphological changes in the vicinity of the filament were analyzed. The observed oscillations of the plasma along the filament was characterized by an initial displacement of 24 Mm, initial velocity amplitude of 51 km/s, period of 50 min, and damping time of 115 min. We interpret the trigger in terms of poloidal magnetic flux injection by magnetic reconnection at one of the filament legs. The restoring force is caused by the magnetic pressure gradient along the filament axis. The period of oscillations, derived from the linearized equation of motion (harmonic oscillator) can be expressed as $P=\pi\sqrt{2}L/v_{A\phi}\approx4.4L/v_{A\phi}$, where $v_{A\phi} =B_{\phi0}/\sqrt{\mu_0\rho}$ represents the Alfv\'en speed based on the equilibrium poloidal field $B_{\phi0}$. Combination of our measurements with some previous observations of the same kind of oscillations shows a good agreement with the proposed interpretation.Comment: Astron. Astrophys., 2007, in pres

String Matching and 1d Lattice Gases

We calculate the probability distributions for the number of occurrences $n$ of a given $l$ letter word in a random string of $k$ letters. Analytical expressions for the distribution are known for the asymptotic regimes (i) $k \gg r^l \gg 1$ (Gaussian) and $k,l \to \infty$ such that $k/r^l$ is finite (Compound Poisson). However, it is known that these distributions do now work well in the intermediate regime $k \gtrsim r^l \gtrsim 1$. We show that the problem of calculating the string matching probability can be cast into a determining the configurational partition function of a 1d lattice gas with interacting particles so that the matching probability becomes the grand-partition sum of the lattice gas, with the number of particles corresponding to the number of matches. We perform a virial expansion of the effective equation of state and obtain the probability distribution. Our result reproduces the behavior of the distribution in all regimes. We are also able to show analytically how the limiting distributions arise. Our analysis builds on the fact that the effective interactions between the particles consist of a relatively strong core of size $l$, the word length, followed by a weak, exponentially decaying tail. We find that the asymptotic regimes correspond to the case where the tail of the interactions can be neglected, while in the intermediate regime they need to be kept in the analysis. Our results are readily generalized to the case where the random strings are generated by more complicated stochastic processes such as a non-uniform letter probability distribution or Markov chains. We show that in these cases the tails of the effective interactions can be made even more dominant rendering thus the asymptotic approximations less accurate in such a regime.Comment: 44 pages and 8 figures. Major revision of previous version. The lattice gas analogy has been worked out in full, including virial expansion and equation of state. This constitutes the main part of the paper now. Connections with existing work is made and references should be up to date now. To be submitted for publicatio

Bayesian Centroid Estimation for Motif Discovery

Biological sequences may contain patterns that are signal important biomolecular functions; a classical example is regulation of gene expression by transcription factors that bind to specific patterns in genomic promoter regions. In motif discovery we are given a set of sequences that share a common motif and aim to identify not only the motif composition, but also the binding sites in each sequence of the set. We present a Bayesian model that is an extended version of the model adopted by the Gibbs motif sampler, and propose a new centroid estimator that arises from a refined and meaningful loss function for binding site inference. We discuss the main advantages of centroid estimation for motif discovery, including computational convenience, and how its principled derivation offers further insights about the posterior distribution of binding site configurations. We also illustrate, using simulated and real datasets, that the centroid estimator can differ from the maximum a posteriori estimator.Comment: 24 pages, 9 figure

Site effects of the Roio basin, L’Aquila

During the microzonation studies of the April 6th, 2009 L’Aquila earthquake, we observed local seismic amplifications in the Roio area—a plane separated from L’Aquila city center by mount Luco. Six portable, digital instruments were deployed across the plain from 15 April to mid-May 2009. This array recorded 152 aftershocks. We analyzed the ground motion from these events to determine relative site amplification within the plain and on surrounding ridges. Horizontal over vertical spectral ratio on noise data (HVSRN),aftershock recordings (HVEQ) and standard spectral ratio (SSR) showed amplifications at 1.3 and 4.0Hz on quaternary deposits. Seismic amplifications in the frequency range of 4 and 6Hz were also observed on a carbonate ridge of Colle di Roio, on the northwestern border of the plateau. A small amplification was noticed near the top of mount Luco, another rocky site. Large discrepancies in the amplification levels between methods have been observed for these sites, but the HVSRN, HVEQ and SSR gave similar results at the stations located in the Roio plain. On the rocky sites, the SSR was more reliable than the HVSRN at estimating the transfer function of the site, even if the resonance frequency seemed to be well detected by the latter method.Published809–8234.1. Metodologie sismologiche per l'ingegneria sismicaJCR Journalreserve